You need stable legs to make a powerful swing, but lower-body stability doesn’t require hours in the gym doing Olympic lifts or other complicated exercises. You can build a sturdy platform to swing from in your lounge room.
Not only is it important to hold a golf club correctly if you want to generate power and allow it to “release” through the impact zone, it also reduces the stress placed on the joints of the arm.
Medicine balls are considerably heavier than a golf club, which means you need to recruit more muscle power than your arms can provide if you want to throw one with any force.